Method and apparatus for transmitting a laser signal through fog

ABSTRACT

A method and apparatus for transmitting laser signals through fog, in which a laser signal directed into the fog is amplitude modulated at one or more resonant frequencies of the water droplets forming the fog at such strength as to cause the droplets to burst, thereby decreasing the scattering of the laser signal and increasing the transmission of this signal through the fog.

RIGHTS OF THE GOVERNMENT

The invention described herein may be manufactured, used, and licensedby or for the United States Government for governmental purposes withoutpayment to us of any royalty thereon.

BACKGROUND OF THE INVENTION

The invention relates to a method and apparatus for increasing thetransmission of a laser signal through a fog.

The problem of "seeing through" fog has been a persistent difficulty. Anumber of techniques have been employed in the past to disperse fog orshift to very long wavelengths (far infared or microwaves) to reduce thescatter created by fog droplets. Another method of penetrating fog hasbeen to use very high laser light power to evaporate the fog dropletsand reduce the particle size, thereby reducing the scatter in the pathof the laser beam. Such a technique is quite costly due to amount ofenergy consumed by the evaporation process. The shift to microwavefrequencies avoids the problem but at a tremendous loss in resolvingpower of the object being detected.

SUMMARY OF THE INVENTION

Accordingly, it is a primary object of the invention to provide a novelmethod and apparatus for transmitting laser signals through fog.

It is another object of the invention to provide a method and apparatusfor transmitting laser signals through fog, which requires less powerand is therefore more efficient than other proposed or actual methodsand apparatus for this purpose.

In the method and apparatus described herein, a laser signal directedinto the fog is amplitude modulated at one of the resonant frequenciesof the water droplets forming the fog at such strength as to cause thedroplets having this resonant frequency to burst, thereby decreasing thescattering of the laser signal and increasing the transmission of thissignal through the fog. When the size and distribution of the fogdroplets is known, the modulation frequency can be varied over afrequency range so as to cause most of the fog droplets to burst. Wherethe size and distribution of the fog droplets is not known, themodulation frequency can be varied over a frequency range correspondingto the range and size within which most fog droplets fall. For the sameincrease in laser signal transmission, the amount of energy required todissipate the fog by bursting the fog droplets is many orders ofmagnitude smaller than that required to dissipate the fog by partiallyvaporizing the fog droplets. Also, since the resonant frequency of fogdroplets lie within a sonic and ultrasonic range (10 kHz to 10 MHz),amplitude modulation of the laser signal is easily obtained by existingconventional techniques.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better understood, and further objects, featuresand advantages thereof will become more apparent from the followingdescription of preferred embodiments, taken in conjunction with theaccompanying drawings in which:

FIG. 1 is a histogram of droplet size in a typical liquid-droplet fog;

FIG. 2 is a schematic block diagram of a first embodiment of theinvention; and

FIG. 3 is a schematic block diagram of a second embodiment of theinvention.

DESCRIPTION OF PREFERRED EMBODIMENTS

A fog is a multitude of particles, usually water droplets, suspended inair which reduce visibility to less than one kilometer. Fogs generallyproduce very little or no precipitation, and are thus said to becolloidally stable, that is, there is no marked tendency within them forthe size of some of the droplets to grow rapidly at the expense of theother drops. Fogs are characterized by relatively small size drops,predominately much less than 100 microns in diameter. The concentrationof droplets in fog rarely exceeds 100 per cubic centimeter, and theliquid water contents are usually of the order of hundredths of a gramper cubic meter and less. The radius of most fog droplets is between twoand eighteen microns. A characteristic feature of the fog dropletsize-distribution is the existence of a maximum for some droplet radiusa_(m), as shown in FIG. 1.

If an electric field E is applied to a water drop in free space, thedrop will expand along the direction of the field E. If the direction ofthe field is reversed, the drop still expands along the field. Thus, theforce F on the drop is proportional to the square of the electric fieldE, or

    F=KE.sup.2                                                 (1)

where K is a constant dependent on geometry, dielectric constant, etc.

If an amplitude modulated laser beam is utilized to generate theelectric field E, the average force F(t) on the water drop over theperiod of the laser frequency T_(L), which is very short compared to theperiod of the amplitude modulation, is given by the followingrelationship, ##EQU1## If the electric field E of equation 1 is selectedas

    E(t)=E.sub.o cos ωt[1+ε.sub.M cos ω.sub.M t](3)

where ω is the frequency of the laser, ω_(M) is a modulation frequency(ω_(M) >>ω), and ε_(M) is the depth of modulation, then ##EQU2## If thisvalue of E² (t) is used in Equation (2), then ##EQU3##

Thus, it is seen that the force F(t) on the water drop will contain themodulation frequency ω_(M) along with twice the modulation frequency 2ω_(M) as well as a constant term K.

If an amplitude modulated laser beam, such as produced by a CO₂ laser,is used to generate the electric field given by equation 3 above, and ifwater drops of uniform size are immersed in this field, the water dropsthen resonate when the modulation frequency ω_(M) of the electric fieldE(t) matches the mechanical resonant frequency ω_(n) of the droplets,which is derived by Lord Rayleigh and is defined as follows: ##EQU4##where n is the resonance mode number, τ is surface tension, ρ is thedensity and a is the drop radius. Thus for the dominant oscillation mode(n=2), ##EQU5##

As shown in Equation (5), the strength of the force acting on the waterdroplets will depend on the power in the laser beam through the factorE². If the power in the laser beam is high enough, the drops will breakand reduce the scattering of the laser beam. This reduction ofscattering can be shown quite simply by using the Rayleigh formula forthe scattering cross section, σ, as follows:

    σ=A a.sup.6 /λ.sup.4                          (7)

where A=160π⁵ δ² /3(δ=(ε-1)/(ε+2), ε is the dielectric constant), a isthe drop radius and λ is the wavelength of the laser light. Theattenuation I of a beam of light traveling through a length, L, of thefog particles is given by

    I=I.sub.o e.sup.-Γ.sbsp.o.sup.L                      (8)

where Γ_(o) =N_(o) σ with σ being given by equation (7) and N_(o) beingthe number of droplets per unit volume. Thus if all the droplets werebroken in half, their new radius would be a/2^(1/3) but their numberwould be doubled, so that the new attenuation coefficient, Γ, would beΓ=Γ_(o) /2.

Since the stored energy of each droplet, W_(s), associated with thesurface tension, λ, (λ=72.75 dynes/cm for water at 20° C.) is

    W.sub.s =4πγa.sup.2                               (9)

then the final surface energy W' for the resultant two drops is

    W.sub.s '=2.sup.1/3 W.sub.s                                (10)

Or ΔW_(s) =[2^(1/3) -1]4πγa²

and this increase in energy ΔW_(s) must be supplied by the laser beam.

If the reduction in drop size is accomplished by evaporating the dropsto reduce the attenuation coefficient by the same amount (Γ_(o) /2),from equations (7) and (8) the required size of the final drop will bea/2^(1/6), assuming the number of particles remain constant during theevaporation process. The energy ΔW_(v) which will have to be supplied bythe laser beam will then be ##EQU6## where ρ is the density and L_(o) isthe latent heat of vaporization (for water L_(o) =540 calorie/gram or2259.36 joules/gram). Using the values γ=72.75 dynes/cm and L_(o)=2259.36 joules/gram in equations (10) and (11),

    ΔW.sub.s =2.376×10.sup.-5 a.sup.2 joules       (12)

    ΔW.sub.v >2.772×10.sup.3 a.sup.3 joules        (13)

if a is measured in cm.

Using equations (12) and (13), the amount of energy required to reducethe scattering by identical factors for a 1 micron drop of water is

    W.sub.s ≃2.38×10.sup.-13 joule

and

    W.sub.v ≃2.77×10.sup.-9 joule

Similarly, the amount of energy required to reduce the scattering byidentical factors for a 100 micron drop of water is

    ΔW.sub.s ≃2.38×10.sup.-9 joule

and

    ΔW.sub.v ≃2.77×10.sup.-3 joule

Thus, it is seen that in any practical region of drop size the amount ofenergy required to dissipate the fog is many orders of magnitude smallerif the droplets are broken as compared to vaporized.

In the embodiment of FIG. 2, a high power laser 10, such as a CO₂ laser,generates a laser beam 12 which is directed into a fog 14. The laserbeam 12 is modulated by a modulation controller 16 at at least one ofthe resonant frequencies of the water droplets forming the fog at suchstrength as to cause bursting of the fog droplets whose mechanicalresonant frequency corresponds to the modulation frequency. Preferably,the modulation frequency will be swept over a range of frequencies so asto burst most of the droplets forming the fog. For example, since theradius of most droplets in a fog is between two and eighteen microns,the modulation frequency can be continuously swept from 1.35×10⁶ Hz to50.0×10³ Hz, corresponding to the mechanical resonant frequencies of 18micron radius and 2 micron radius water droplets, respectively. In thisway, most of the droplets forming a fog will be split one or more timesinto droplets having a radius of less than 2 microns. Where the dropletsize-distribution of the fog is known, the frequency range over whichthe modulation frequency is swept can be accurately set so that most ofthe fog droplets are burst one or more times to thus reduce the averagedroplet size and increase the transmission of the laser beam 12 throughthe fog 14.

In the embodiment of the invention shown in FIG. 3, the fog dropletsize-distribution is determined in accordance with the method andapparatus described in our U.S. Pat. No. 4,211,487, issued July 8, 1980,which is hereby included herein by reference. In addition to the highpower laser 10 and the modulation controller 16, this preferredembodiment includes a sampling laser 18, a scattered beam detector 20, amicroprocessor 22, and a display 24. The modulation frequency of thelaser beam 12 produced by the laser 10 is selectively variable over apredetermined frequency range, as determined by the microprocessor 22controlling the modulation controller 16. The system in FIG. 3 isoperated in a first mode to determine the droplet size-distribution, andthereafter in a second mode to disperse the fog along the path of thelaser beam 12.

In the first mode of operation, the laser 10 is operated to generate anamplitude modulated laser signal having sufficient strength to causedroplets in the laser path having a resonant frequency corresponding tothe modulation frequency to resonantly elongate and contract. Themechanically oscillating droplets present varying reflective surfaces tothe impinging sampling laser beam 26, which results in a varyingintensity for a reflected sampling laser beam. Thus, the intensity ofthe reflected sampling laser beam is in turn modulated by the resonatingdroplets. The modulation component of the reflected sample laser beam 26is monitored by the detector 20. Assuming that each resonating droplet,regardless of size, contributes an identical amount to the detectedmodulation component, a quantitative measure of the number of dropletsof a particular size is provided at each modulation frequency ω_(M).This quantitative measure is produced by the microprocessor 22, as datafor each modulation frequency ω_(M) is obtained, and a size-distributionprofile is obtained.

In a second mode of operation, the field E_(o) and/or the depth ofmodulation ε_(M) is increased so that droplets in the path of the laserbeam having the same mechanical resonant frequency ω_(n) as themodulation frequency ωhd M will mechanically elongate and burst intosmaller droplets. The modulation frequency range is determined by themicroprocessor 22. For example, for the typical dropletsize-distribution shown in FIG. 1, the modulation frequency could bevaried by the microprocessor 22 between 25.8×10³ Hz corresponding to adroplet radius of 28 microns, and a frequency of 478×10³ Hzcorresponding to a droplet radius of 4 microns. Alternatively, thedroplet size-distribution could be observed by an operator at thedisplay 24, and the modulation frequency selected and varied manually bythe operator during the second mode operation of the apparatus.

For the purpose of example, a CO₂ high-power linearly-polarized,amplitude-modulated cw laser can be used for the laser 10, and a He-Necw laser can be used for the sampling laser 18.

Since there are many variations, modifications, and additions to thespecified embodiments of the invention described herein which would beobvious to one skilled in the art, it is intended that the scope of theinvention would be limited only by the appended claims.

What is claimed and desired to be secured by Letters Patent of theUnited States is:
 1. A method of transmitting a laser signal through afog of liquid droplets, comprising the steps of:generating a continuousunidirectional laser signal in the form of a laser beam at a lasercarrier frequency ω; modulating the amplitude of the laser beam at atleast one modulation frequency ω_(M) which is much less than the carrierfrequency ω and which is equal to one of the expected mechanicalresonant frequencies of the droplets forming the fog, wherein theamplitude-modulated laser signal generates a unidirectional electricfield along the laser beam path which is defined by the relationship

    E(t)=E.sub.o cos ωt (1 +e.sub.M cos ω.sub.M t)

where E_(o) is the peak amplitude of the electric field which is afunction of the maximum power density of the laser beam, and e_(M) isthe depth of modulation of of the electric field which is a function ofthe depth of modulation of the laser beam, the power density andmodulation depth of the laser beam being selected such that the forceacting on liquid droplets disposed in the laser beam path as a result ofthe electric field is sufficient to cause droplets having a mechanicalresonant frequency ω_(M) to burst; and directing the amplitude-modulatedlaser beam into the fog, whereby the electric field generated by thelaser beam causes liquid droplets disposed in the laser beam path andhaving a mechanical resonant frequency equal to the modulation frequencyω_(M) to burst, decreasing the scattering of the laser beam andincreasing the transmission of the laser signal through the fog.
 2. Amethod, as described in claim 1, wherein the step of modulating theamplitude of the laser beam comprises the further step of varying themodulation frequency over a frequency range corresponding to theexpected range of sizes of most of the droplets forming the fog.
 3. Amethod, as described in claim 1, which further comprises a first step ofdetermining the size and distribution of the droplets forming the fog.4. A method, as described in claim 3, wherein the step of modulating theamplitude of the laser beam comprises the further step of varying themodulation frequency over a frequency range corresponding to the rangeof sizes of most of the droplets forming the fog.
 5. Apparatus fortransmitting a laser signal through a fog of liquid droplets,comprising;signal generating means for generating a continuousunidirectional laser signal at a laser carrier frequency ω in the formof a laser beam directed into the fog; and signal modulating means formodulating the amplitude of the laser beam at least one modulationfrequency ω_(M) which is much less than the carrier frequency ω andwhich is equal to one of the mechanical resonant frequencies of thedroplets forming the fog, wherein the amplitude-modulated laser signalgenerates a unidirectional electric field along the laser beam pathwhich is defined by the relationship

    E(t)=E.sub.o cosωt (1+e.sub.M cos ω.sub.M t)

where E_(o) is the peak amplitude of the electric field which is afunction of the maximum power density of the laser beam, and is e_(M) isthe depth of modulation of the electric field which is a function of thedepth of modulation of the laser beam, the power density and modulationdepth of the laser beam being selected such that the force acting onliquid droplets disposed in the laser beam path as a result of theelectric field is sufficient to cause droplets having a mechanicalresonant frequency 24 ω_(M) to burst, decreasing the scattering of thelaser beam and increasing the transmission of the laser signal throughthe fog.
 6. Apparatus, as described in claim 5, wherein the signalmodulating means comprises means for varying the modulation frequencyω_(M) over a preselected range of frequencies.
 7. Apparatus, asdescribed in claim 6, which further comprises measuring means fordetermining the size and distribution of the droplets forming the fog.